| Title of paper:
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Approximate solution of intuitionistic fuzzy differential equations by using Picard's method
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| Author(s):
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| R. Ettoussi
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| Sultan Moulay Slimane University, Laboratory of Applied Mathematics and Scientific Computing, Department of Mathematics, Beni Mellal, Morocco
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| razika.imi@gmail.com
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| S. Melliani
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| Sultan Moulay Slimane University, Laboratory of Applied Mathematics and Scientific Computing, Department of Mathematics, Beni Mellal, Morocco
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| saidmelliani@gmail.com
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| L. S. Chadli
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| Sultan Moulay Slimane University, Laboratory of Applied Mathematics and Scientific Computing, Department of Mathematics, Beni Mellal, Morocco
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| sa.chadli@yahoo.fr
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 2, pages 52–62
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| DOI:
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https://doi.org/10.7546/nifs.2018.24.2.52-62
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| Download:
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 PDF (216 Kb Kb, File info)
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| Abstract:
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Our main result in this paper is to find the power series solution of an intuitionistic fuzzy differential equation [math]\displaystyle{ x'(t) = f(t, x(t)), x({t_0}) = {x_0} }[/math] by using successive approximation method and we prove that the approximate solution converge uniformly in t to the exact solution. Finally, we illustrate this result with a numerical example.
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| Keywords:
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Intuitionistic fuzzy solution, Intuitionistic fuzzy number, Picard's iterative method.
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| AMS Classification:
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34A07, 03E72
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| References:
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- Atanassov, K. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.
- Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Springer Physica-Verlag, Heidelberg.
- Ettoussi, R., Melliani, S., & Chadli, L. S. (2017) Differential equation with intuitionistic fuzzy parameters, Notes on Intuitionistic Fuzzy Sets, 23(4), 46–61.
- Ettoussi, R., Melliani, S., Elomari, M., & Chadli, L. S. (2015) Solution of intuitionistic fuzzy differential equations by successive approximations method, Notes on Intuitionistic Fuzzy Sets, 21(2), 51–62.
- Keyanpour, M., & Akbarian, T. (2014) Solving Intuitionistic Fuzzy Nonlinear Equations, Journal of Fuzzy Set Valued Analysis, 2014, 1–6.
- Melliani, S., & Chadli, L. S. (2001) Introduction to intuitionistic fuzzy partial differential Equations, Notes on Intuitionistic Fuzzy Sets, 7(3), 39–42.
- Melliani, S., Elomari, M., Chadli, L. S., & Ettoussi, R. (2015) Intuitionistic Fuzzy metric spaces, Notes on intuitionistic Fuzzy Sets, 21(1), 43–53.
- Zadeh, L. A. (1965) Fuzzy set, Information and Control, 8(3), 338–353.
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